Ari,

I think (however from your screenshot I can't tell exactly) your problem is that you need to switch back to "object mode".

Remember Maya has several modes "Object & Component" seperate from "Component" Maya has several SubD modelling modes "Standard" and "Poly".

Try switching back to "Object" mode (F8) that should remove your "components" being visible and should have only the entire object(s) highlighted. Moving will now move the entire model (as opposed to components such as verts, faces, etc)

Hopefully this is your problem - otherwise something really crazy is happening....